The Method of Moments (MoM) is a popular frequency domain technique used in computational electromagnetics and is also used to solve a wide range of problems, from circuit simulation to radar signatures of airplanes and ships. The method employs models of the boundaries where discrete objects touch. In particular, these boundaries are discretized into a plurality of patches, then an excitation is applied, and then the currents/charges on the patches are obtained. From these currents/charges obtained from the patches, many useful quantities can be calculated. These useful quantities include, but are not limited to: scattering patterns, capacitance, and inductance and radar cross sections.
When one has N patches, there are N2 interactions that take place among the N patch elements. As a result, a matrix of size N×N can be obtained for this situation. The N×N matrix represents a system of linear equations, such as A*x=b, where: A is the N×N matrix; b represents the excitation, and x represents a matrix of the values of the current/charge on the various patches. The N×N matrix represents a system of linear equations that is typically quite dense in nature. A dense system of equations may consist of hundreds to many thousands of unknowns in real and/or complex form.
The preferred solvers for the MoM are: (1) direct solution via Lower-Upper (LU) factorization, followed by (2) iterative methods (e.g., Generalized Minimal Residual (GMRES) method). However, a bottleneck may exist in using these preferred solvers in attempting to solve the dense system of linear equations discussed above in that these solvers, as implemented in prior implementations, may generally become impractical as the problem size grows. That is, though they provide more accurate answers, the LU and GMRES methods are often overlooked for all but the most trivial problems. As an alternative, the so-called “accelerated methods,” which generally sacrifice accuracy and applicability for speed, are used instead.
However, a limitation of these accelerated methods is that they are less accurate, and they are, therefore, typically used only as a last resort. Thus, in the background art, LU and iterative solvers such as GMRES are preferred for small to medium sized problems, and accelerated methods are preferred for very large problems. Therefore, in consideration of the above discussion, there is a need in the art for solvers for the MoM that are fast, accurate and can be applied to larger problems.